Suggestions for road bike rental

I know this has been asked a few times but a lot of the information seems out of date, and I figured it would be worth trying again!
I'll be in Tokyo in late August/early September with my partner and we're planning a trip to Mt Fuji. I'm determined I'm going to somehow get hold of a road bike and ride up as much as I can, most likely up the main road (I know it's the busiest) to the 5th station car park.
Anyhow, it seems that renting road bikes in Japan isn't particularly easy, so I'm guessing I'm not likely to find anywhere in the Mt Fuji/Kawaguchiko area that will have one. It seems my options are, in decreasing order of preference:
a) Find somewhere that will rent me one and send it to somewhere in/near Kawaguchiko (or even Otsuki)
b) Find somewhere in Tokyo where I can either rent or buy used/sell back after, and then either:
1) have it sent to Kawaguchiko
2) take it on the train (my partner, who grew up in Tokyo, is convinced this is impossible - the trains would be too crowded)
3) ride part of the way, to get away from the busiest parts of Tokyo, then catch a train from there.

Obviously it's going to be somewhat expensive, but the last resort option of taking my own bike (from Australia) doesn't really appeal to me, given for most of the 3 week trip I wouldn't be able to use it, and don't really want to have to cart it about, and doesn't solve the problem of getting it to Kawaguchiko.

As for the bike itself, any sort of road bike (doesn't have to be carbon) with suitable gearing is fine, doesn't have to be super fancy.

Has anyone here used the luggage sending service in Japan (there's one with the Black Cat logo that we've used before, they seem to be pretty reliable) for sending bikes?